Weighted norm inequalities for commutators of Littlewood-Paley functions related to Schr\"odinger operators

Abstract

Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while the nonnegative potential $V$ belongs to certain reverse H\"{o}lder class. In this paper, we establish some weighted norm inequalities for commutators of Littlewood-Paley functions related to Schr\"odinger operators.